The present invention relates to a method for efficiently computing the value of sine or cosine transforms of a bounded analytical function. Specifically, a method for efficiently computing the value of a transform using a digital computer is described.
In various engineering disciplines the need arises for efficiently evaluating sine or cosine transforms of a bounded analytic function. The sine or cosine transform has been traditionally evaluated using a digital computer. One such standard computation technique involves the use of a Gauss-Legendre integration as set forth in a text entitled, "Numerical Recipes," by W.H. Press et al.
When computing the sine or cosine transforms using the prior art digital computer techniques adapted to execute a Gauss-Legendre integration, computation time is excessive, requiring up to 10,000 CPU seconds using a modern digital computer. The lengthy time is a significant disadvantage in using the sine or cosine transforms.
One specific example of the need for efficiently calculating the transform is in the field of MOSFET design. Designers of MOSFET semiconductors would typically use a sine or cosine transform to evaluate the carrier density function (nz) in the semiconductor material. The process of calculating the carrier density function is set forth in a paper co-authored by the inventor, entitled "Quantum Mechanical Screening Current in Silicon MOS Devices."
The traditional way of calculating carrier density involves the calculation of the integral of a periodic function, referred to as the modified Fermi-Dirac integral is set forth in the paper by Slinkman et al. The evaluation of the integral makes it possible to determine not only the current density, but also the related, measurable quantity of gate capacitance for a MOSFET device.
It is a disadvantage to use the prior art technique for digitally computing the Fermi-Dirac integral by utilizing the aforementioned Gauss-Legendre integration. Up to 7200 CPU seconds may be needed in order to calculate only one of several equivalent silicon conduction valleys for a MOSFET device.
Given the computational inefficiencies of the traditional techniques for computing digitally a value of a class of integrals which are bounded over the infinite domain, the present invention provides for a method for efficiently computing the transforms.